Sorry, but you cannot create new factions, you can only have the amount in-game. But, if you wanted, you could try to make the 3 Romans into 3 Greek City states and have only one roman faction...

For this you would need to:

Mod some text files (tutorials can be found on this forum)
Make a unified Rome, and remove senate missions
Possibly make a bigger map, or add some more regions (you would need photoshop for this).

If you have any questions, just post on the modding questions forum and people will help you